Mathletics and the Proficiency Strands

In the Australian Maths Syllabus there are 3 content strands:

• Number and Algebra
• Measurement and Geometry
•  Statistics and Probability

This content is to be explored and developed via 4 proficiency strands:

These are a way of describing ACTIONS rather than subject matter.

These actions are intertwined and they are all equally important.

Let’s look at each proficiency strand more closely:

Historically, the major emphasis in school mathematics instruction has been on rote learning facts and procedures with little attention given to developing an understanding of mathematical concepts that are the foundation of facts and procedures. Solely focussing on rote learning is not the way children build up a robust understanding of maths. In fact it can actually cause much more harm than good.

Rote learning is when you memorise facts or procedures without really thinking about meaning. A example of this is the chanting of times tables facts over and over. Children might be able to recite “…. 4 sixes are 24, 5 sixes are 30, 6 sixes are 36…” and so on all the way through to 12 x 6 but this does not ensure that they have a conceptual understanding of multiplication. Introducing the multiplication operation through relating repeated addition to multiplication, equal groups and as an array helps children develop conceptual understanding or build ‘velcro’ for facts to ‘stick’ to. Providing lots of experiences with making ‘rows of’ or ‘piles of’ manipulatives such as buttons, counters or pop sticks further develops their ‘velcro’.

To be sure, being adept or fluent in recalling facts and procedures is still very important. But without conceptual understanding any knowledge — such as times tables facts — is fragile, easily forgotten and gives rise to misconceptions that can be tricky to undo. Crucial for conceptual understanding is providing experiences for students where they can see how something is related or connected to other things that they know. Connecting ideas is not a linear process, it is much more like a web. This takes time and lots of varied experiences best provided through different resources linked together by the teacher.

Here are some examples of rich content in our eBooks for the development of conceptual understanding:

Our activities provide consolidation of understanding through practice.

Lots of our activities support fluency too.

The Support Centre provides crucial links to prior knowledge.

Fluency refers to procedural fluency which is the ability to carry out procedures flexibly and accurately where factual knowledge comes to mind readily.

Being procedurally fluent is important because it frees up working memory to focus on solving problems.

Robust mathematical skills are learned through both fluency and understanding. A balance of both is vitally important.

Our world famous LIVE Mathletics is our flagship product and makes practising procedural fluency even more fun now that players can see who’s online and invite them to a game!

Children are naturally curious and learn to make sense of their world through exploration, questioning and reasoning. Through reasoning, children connect ideas, gain a deeper conceptual understanding and ultimately enjoyment of mathematics. In short it is through reasoning that they learn that mathematics makes sense.

Effective environments for nurturing mathematical reasoning can be created through deliberately choosing tasks and activities that require reasoning. The teacher’s role in providing opportunities to practise the tools and habits of reasoning is significant.

Mathematical reasoning involves exploring the mathematics at hand and communicating conceptual understanding.

The practice of reasoning underpins all maths learning. To really understand how capable of reasoning students are, teachers need to provide them with appropriate tasks where thy need to apply logic and then ask them how they found the solution.

Magic Symbols 1 is a new style of activity where children have to apply logical reasoning skills. This could also be described as guided problem solving.

Problem solving is a method of teaching that requires children to apply their conceptual understanding and  reasoning skills. It refers to the ability to formulate, represent and solve mathematical problems and the ability to select or devise a plan. Problem solving is what children have to do when they are presented with unfamiliar scenarios or questions and they have to design their own investigations, plan their approaches and apply strategies to get the solution.

We have resources that get children to develop and apply conceptual understanding and reasoning skills in problem solving context.

Problem solving resources

Example of tasks in the Primary eBooks that get children to apply reasoning skills in problem solving context:

Example of tasks in the Primary eBooks that get children to apply reasoning skills in problem solving context:

Hopefully now it is clear to see proficiency strands are actions that are intertwined, and developed over time.

This quote provides a neat summary:

‘Teaching is for learning, learning is for understanding, understanding is for reasoning and applying and, ultimately problem solving.’

http://www.moe.gov.sg/education/syllabuses/sciences/files/maths-primary-2013.pdf